WASHINGTON — Christopher Waller, nominated by President Trump to the Federal Reserve’s seven-member Board of Governors, was confirmed by a narrow margin on Thursday as Republican senators scramble to fill open slots before President-elect Joseph R. Biden Jr. assumes office.

Mr. Waller, a regional Fed research official, had been up for Senate confirmation alongside Judy Shelton, whose long-held preference for some type of gold standard and apparent skepticism of Fed independence hurt her chances of confirmation. Mr. Waller made it through, but just barely, with a nearly party line vote of 48 to 47. Senator Rand Paul, a Kentucky Republican, joined Democrats in voting against Mr. Waller.

Mr. Waller’s selection means that Mr. Biden will take office with a Fed stocked with picks from Mr. Trump, who has now chosen five of the central bank’s six sitting officials, including appointing Jerome H. Powell as its chair. The board will have one remaining open slot if Ms. Shelton is not confirmed. While the sitting governors have varying time left in their 14-year terms, Mr. Waller was appointed to an unexpired slot that stretches through early 2030.

The White House announced that it would tap Mr. Waller and Ms. Shelton in mid-2019, but their nominations — long treated as a pair — faced a roller-coaster confirmation process as senators grappled with misgivings over Ms. Shelton. Mitch McConnell, the Senate majority leader and a Republican of Kentucky, tried but failed to bring her nomination to a vote in November.

Her path to confirmation became even less likely given the changing makeup of the Senate. Senator Mark Kelly, the newly elected Democrat from Arizona, was sworn in this week, and his likely no vote could kill Ms. Shelton’s razor-thin chance of passing, because she already faced opposition from several Republicans. Senator John Thune, Republican of South Dakota, told reporters that Ms. Shelton’s confirmation is “unlikely” after the changeover.

Though he was a conventional pick for the job, Mr. Waller’s confirmation passed by the narrowest margin of any governor going back to at least 1980 and probably ever, based on data collected by a George Washington University professor, Sarah Binder.

The partisan rancor shows how the process of appointing Fed governors — once drama free — has changed over the past decade. Both Mr. Trump and former President Barack Obama struggled to get nominees on the Fed board as political fights have erupted over who should fill seats on the powerful body, which plays a central role in setting interest rates and in shaping financial regulation.

It also underlines the unusual path Mr. McConnell took in trying to push Fed officials through confirmation so late in the game. Mr. Waller is the first nominee ever confirmed during a lame-duck session, the period after an election but before a new administration enters the White House, according to the Fed historian Peter Conti-Brown.

“Everything has become hyper-politicized, and the Fed is no exception,” said Mark Spindel, who with Ms. Binder wrote a book on politics at and around the Fed. “Filling those spots with Trump appointees just limits what Biden can do.”

The Fed’s Washington-based board members hold constant votes on monetary policy, while most of the 12 regional bank presidents rotate in and out of four voting seats. The Federal Reserve Bank of New York is the exception, holding a permanent vote. The board members, called governors, also vote on the regulations that govern the nation’s largest banks.

Interest-rate setting is usually not a partisan exercise, and policy preferences do not split cleanly along ideological lines. But bank oversight tends to be more political, with Republicans favoring lighter oversight and Democrats pushing for more stringent rules.

Despite the drama, Mr. Waller’s confirmation was received as good news by many in the central banking community.

He is a seasoned economist who has worked in academia and, most recently, as research director at the Federal Reserve Bank of St. Louis.

Mr. Waller’s research has covered topics including central bank independence — “the key tool to ensure a government will not misuse monetary policy” — and he has laid out a rationale for keeping borrowing costs cheap when prices are increasing slowly, as they have been in recent years. The Fed raises or lowers interest rates to slow or speed up the economy, hoping to keep inflation slow and stable while maximizing employment.

Before joining the Fed in 2009, Mr. Waller was a professor in the economics department at Notre Dame. He has a doctorate from Washington State University. It is not clear whether he will be installed at the Fed in time for the central bank’s Dec. 15-16 meeting.

“He’s been an excellent research director,” Robert S. Kaplan, the president of the Federal Reserve Bank of Dallas, said of Mr. Waller, calling him an “excellent economist” with a “keen mind.”